Stabilization of fractional neutral systems with one delay and a chain of poles asymptotic to the imaginary axis

In this paper we consider the stabilizability of fractional single delay systems of the neutral type which have a chain of poles clustering the imaginary axis. These systems are H
∞
-stabilizable, however we prove here that the subclass of H
∞
-stabilizing controllers which are given in terms of polynomials in the Laplace variable s, s
^v
and e
^−ST
(where v is a rational, v ∊ (0,1) and τ real positive is the value of the delay) cannot move the chain of poles far away from the imaginary axis in the left half-plane as they necessarily introduce stable chains of poles clustering the imaginary axis in the closed-loop. Some examples and simulations are given.